i cam across this puzzle, we are supposed to find out the total number of squares present in this picture...
as being a computer programmer i designed a algo in my head for the solution and did a dry run in my head as well.
Start counting by square with highest dimension and then decrement the dimension by 1 step by step and at every decrement iterate the whole graph for matching dimensions & count them untill the dimension becomes zero... so
4x4 squares = 1
3x3 square = 4
2x2 squares = 9
1x1 squares = 16
that makes 30 squares..
i was thinking isn't there a mathematical formula to calculate the number of sub-squares in a given squared-section of graph?
p.s.
i can see a pattern, here in the above square(4) + square(3) + square(2) + square(1) but i don't enough skills in discrete mathematics & numerical analysis to bring it down to an equation or formula but i am sure the formula already exists
It is $$\sum_{k=1}^{n} k^2 = \frac{1}{6}n(n+1)(2n+1)$$
which can be prooved via induction.
For $n=4$ this will give you $\frac{1}{6}\cdot4\cdot5\cdot9=30$